The Dynavox LW6004/BR-1 cabinet with high pass filter allowed 50 watts but there was a hump in the bass response (see the Good bass from a low Xmax driver page). Depending on how much bass you like this would be OK, but if you want a flat response lowering the Qes to 0.5 in Winisd gives the desired output. We can electronically change Qes and hence Qts by means of a negative output resistance amplifier. I figured a Qts of 0.7 meant a Qes of 0.78, see below to see how.

Thanks to Brian Steele on this link there is a formula for the relationship source resistance vs Qes:

As Thiele pointed out in his 1961 paper positive current feedback can provide a negative amplifier output resistance and the circuit shown uses this to generate -2 ohms. Positive feedback is used in oscillators and if you are too greedy with the amount of negative resistance the circuit will oscillate. If you try and eliminate all the voice coil resistance the circuit will hoot.

Op-amp U1 is a audio power amp like the LM1875, TDA2030 or LM3886 and U2 is an audio op-amp like the TL072 or NE5532. U1 and U2 need the usual power supplies and decoupling and U1 needs a zobel network to make it work. R8 is the loudspeaker.

Fig1 shows the gain suitable for the power amps mentioned above. How to prove the circuit is generating negative resistance. Making R8 2.05 ohms gives a big peak in the output showing that the net resistance is zero and the gain is more or less infinite (Fig2). It also shows where the feedback is 360 or 0degrees which by luck (or design) happens to be at the box tuning frequency.

Fig 1 Gain response

Fig 2 Gain response with R8 as 2.05 ohms

Given a random drive unit and a random vented box enclosure, can we match them? Bass reflex enclosures usually have to be closely matched to the drive unit. The drive unit has 3 parameters needed for vented box design, the Resonant frequency Fs, the compliance Vas and the Qts. Since the cabinet size is approximately a function of the Qts cubed, it is very dependent on the value of Qts. This technique effectively lowers the Qts to suit a smaller cabinet than normal. The other way of using a smaller cabinet is a variovent but in my opinion that technique is difficult to control.

To go back to the old ways of doing things, Hoge came up with some formulas to make vented box design easier these are:

Vb = 15 X Vas X Qts^2.87

F-3 = 0.26 X Fs/Qts^1.4

Fb = 0.42 X Fs/Qts^0.9

If you take my Mission CP168 with its 0.42 Qts, 0.445 Qes, 9.2 Qms, 23.8 litre Vas , Fs of 47.4Hz, Re of 7.5 and plug it into the equations you get a box size of 29.6 litres which is bigger than the 11 litre box I want to use. What Qts is required for the 11 litre cabinet ?

Rearranging the first equation

Vb/(15 X Vas)= log(base Qts)2.87 which can be done on the calculator by pressing inv before x^y key

The above link shows that the renowned speaker engineer Keele was the originator of the Hoge formulae. I did a similar analysis to the CP168 for the LW6004 and the Qts came out at 0.4 Fb came out at 50Hz . Winisd showed the excursion would only take a 15W amp and needed a 44Hz 3rd order HPF Butterworth which from my table in Xmax problems is this:

So the negative resistance amp can be as above. A suitable device would be the LM1875 and the other half of the op-amp could be used for this filter which gives a 54Hz -3dB response for the overall system.

🆕 Another way of reducing the box size required is to use an isobaric configuration which halves the box size, at the expense of needing another driver. Here is a sketch of how to use a twin subwoofer box in an isobaric configuration. The easiest way to make the recessed blanking plate is to cut the woofer aperture square so the recess can be square. Two negative resistance amplifiers and the Isobaric idea below could be used for the Parts Express 299-1018 drivers and the 260-646 cabinet. The sketch is not to scale, there should be a one inch separation between the old and new front baffles. I modelled the design in Unibox which has on its right hand side a “Drive unit configuration” box. If you select “2 drive units in series compound” it works out the isobaric results. To get a flat response the design needs more negative resistance than the circuit above gives. Also the design is ported, contact me via the comments box below for further details.

Channel 4 recently did a great programme about the construction from scratch of a working replica of the original Tank. My Grandfather was a pattern maker for Fosters of Lincoln so was involved in the original. Pattern makers make wooden patterns for castings which are made by the sand- box process.

The story begins in 1998 when Phillipe Gorzchinsk of Flesquieres searched for and found a buried Tank named Deborah. He also found the Grandson of the Tank Captain, Tim Heap.

Thorsten Brand did a great job on the original CAD drawing for his modelling, using the Tank found by Phillipe as a reference. This was turned in to a product by JCB.

A couple of things intrigued me; the serious plug welds used to join the sheets together. OK for this application but do they use that technique for load bearing structures? Pictures of the sides showing the joining strips

Also the bearing failure. Possible weakness of the original design?

Guy has inherited the mantle of Engineering presenter from Fred Dibnah. Fred wouldn’t have liked the fake rivets. But you need the tooling and the time for rivets!

Stephen Machaye and the volunteers at the Norfolk Tank museum installed a Rolls Royce B60 inlet over exhaust valve engine and a tractor gearbox and axles. Chasestead of Letchworth made a lot of the component parts needed. Overall a great effort in the time available. Stephen and Guy with the completed tank Deborah 2 at Cambrai:

In celebration of 50000 hits, a lot of reads but not much comment, what it is to have the gift of exposition! Anyway in honouring the occasion, I offer the following.

You cannot get good deep bass from a Woofer with low Xmax, right. Wrong, it can be done and here is a way to do it. Thiele in 1961 realised that the equivalent circuit of a bass reflex speaker was a fiIter. Filter development is a method of selecting the poles (and possibly zeros) of a transfer function to meet a particular design criterion. Thus was born the scientific way of doing speaker design, Thiele-Small parameters and the concept of alignments, as in aligning filters.

In the old days you looked up alignments in tables . A bass reflex is a forth order filter. I was fascinated by the sixth order alignments which offered bass extension and control of the excursion by adding an external high pass filter. An underdamped second order filter has boost and can compensate for the drop off in frequency response at low frequencies. Because the speaker has to be active, the design has not been popular until recently for sub-woofer use.

The cone excursion on a bass reflex is at a minimum at the box tuning frequency determined by the port. I realised that if you made the external boost filter peak at the port box tuning frequency , it would minimise the excursion. I did a design which worked well, then I discovered Don Keele’s paper describing the idea scientifically.

The two equations (possibly the 2 simplest equations in the whole of speakerdom!) describing the Keele alignment are these:

Vb=4.1 X Qts2 X Vas

Fb=f3=faux=0.3fs/Qts

Keele applies a filter with 6db boost at the port frequency and this is also the -3dB response limit. These are good starting point for a design. The equations are approximations so it is worth checking using a modern computer program. Winisd is an excellent program for this type of design as you can call on a peaking filter and observe the cone excursion. In my case to keep the twin peaks of cone excursion level and below the Xmax limit I had to offset the external filter upwards from 44Hz to 50Hz resulting in a slight drop of response which I corrected by making the boost 8db.

System response showing 44Hz 6dB peak filter and 50Hz 8dB filter:

Cone excursion with the 2 filters

Filter response of the 2 filters

I looked up the damping factor needed for 8db boost in Don Lancasters Active filter cookbook. Fig.3.25 gave me a figure of 0.4. I used the Japanese filter website to come up with a circuit.

However when I simulated the design I got 4dB boost. So I used a figure of 0.2 as damping factor and got the 8 dB boost and this circuit:

Such a simple circuit to solve all those problems! You do need to drive the speaker with a good power amplifier capable of supplying current at the peak frequency. The low frequencies and small boxes allowed by the technique give a port problem. The long port typically required is difficult to realise. I am going to use the speaker stand as a port tube.

I noticed enviously that the Dynavox drivers and the BR-1 enclosures at Parts express were available at a reasonable price. I wondered if the Keele alignment would work for this combination. I plugged the numbers into Winisd, but alas the system would only work up to 5 watts input before Xmax was exceeded. Ye cannae change the laws of physics Cap’n.

So I tried finding a filter that would work up to 50 watts input and came up with a 3rd order Bessel filter with 70Hz cutoff which gives this response similar to the famed LS3/5a but louder.

The cone excursion

I used Uwe Beis filter design page here to come up with an actual filter which nearly matched the graph in Winisd. The cutoff frequency in Winisd is at -6dB whereas the cutoff on Uwe’s site is at -3dB so you have to find -3dB on the Winisd graph and enter that value on Uwe’s site. A better match is obtained if R1 is 22k and R3 is 18k

Note that the port would need changing, to a a larger diameter shorter port tuned to 70Hz. It would be best to use the round rather than the truncated driver and easier to surface mount it. Also according to the Baronettes project the actual Qts is higher at 0.7, in which case the bass goes up 1dB. By the way the driver is the LW6004.

A remarkably cost effective 3 way active circuit is due to Egerton in WW Circuit ideas, Jan 1988. A subsequent analysis by Brian Pollard in WW Feedback July 1988 showed a slight error in Egerton’s analysis but despite that the circuit is adequate. As given the crossover frequencies are 363 Hz and 1.456 kHz. Egerton found he needed a 200pF capacitor across R5 to suppress high frequency oscillation. The midrange filter is a maximally flat type. I haven’t tried this circuit myself as I have only just found it. Such an elegant circuit demands a decent implementation. However the mid-range driver needs to be high quality and ATC domes do not come cheap! A 2 way design could be made by eliminating the woofer components.

The resistor values given are exact presumably so you can see the relationships. Putting the nearest E24 series values slightly changes the results. I scaled the resistor values to the highest I would be comfortable with. That also gives the lowest capacitor value.

Try R1,2,3,4 &6 as27k, R5 &13 as 16k, R12 10k, R8 68k, R10 39k all Cs 8.2n. If the Cs are made 4.7n the crossover frequencies are 655 and 2.675kHz, which is suitable for the Faital pro 3FE22 I want to try.

The circuit appears to be a minimalist form of the State variable filter. The tweeter circuit unusually uses differentiators and an op amp is saved by combining the summing functions. Rod Elliots adjustable version of the filter (an analogue DCX2496!) is explained here:

There is also a good analysis by Linkwitz on his site. The other John K used a Dayton RS52 in one of his designs, which might be an appropriate mid-range unit. However it would need a notch filter to get rid of the breakup spike. Talking of the RS52 this project uses it:

Although the designer does not mention it, the crossover looks “Duelundish” to me!

Using Ltspice, I summed the outputs in simulation by using a simple mixer circuit. That showed that the polarity of the mid had to be inverted as Pollard had noticed, also that the mid out was 3db more than normal which could be compensated by the mid amplifier of course.

An easier way to sum the outputs is to use Plot settings/Add trace then in the “expressions to add” window, add the woofer and tweeter outputs (+sign) and subtract the middle output. This shows an underdamped response. Reference to Don Lancasters Active Filter cookbook which has a good section on State variable filters showed that R5 could be tweaked to vary the damping . With R5 at 7.1k the mid response is a plateau but 4.4dB above nominal.

With R1,2,3,4 & 6 as 13k, R5 9.1k R12 3.6k R13 6.2k R8 47k and R10 27k also all Cs 10n you get crossover frequencies at 447 and 3.57k suitable for the venerated ATC mid dome. If R5 is made 12k you get the plateau response with a 4.4dB lift.

There is a good discussion on the Duelund here particularly post 26 by Jon Marsh

Jons piece plus my sims showed that the mid output should be below the woofer and tweeter outputs. To get a level sum on the original circuit, I found it easier to raise the woofer and tweeter levels by raising R2 & R6 to 18k and making R5 9k. Mid in and out of phase plot with this mod:

I am sufficiently intrigued by this circuit that I am going to try it with a HiVi TM1a mid/tweeter combination plus my long suffering CP168. Crossover points would be 1.4K and 5.5K

The electronic filter slopes are also the target acoustic slopes, but the drive units will not perfectly convert their electric inputs to acoustic outputs. It is the amount of tweaking needed, the less the better, which will determine the success of this filter topology.

I noticed that Parts Express were offering the RS52 at a sale price of $40 so I came up with an active notch filter to add to the Active Duelund circuit . It uses a bridged T configuration with positive feedback to increase the Q. It needs setting up by having a signal generator that is set up to run at the break-up spike frequency by monitoring the break-up spike with a microphone and a scope. Then insert the filter and tweak the pot for minimum signal.

The usual provisos about supplies and decoupling for the op-amp apply In addition the input needs to be at 0V. If it is AC coupled it needs a 150k resistor to ground to provide bias for the op-amp

I have had second thoughts about the RS52 notch filter. Rather than have the hassle of setting a pot I have widened and deepened the notch so that no setting is necessary. R1 is now 3.3k and R3 is 220 ohm The pot is replaced by a short circuit.

Another interesting choice for the mid/tweeter combination would be the Tannoy coaxial which meets Duelunds timing criteria. Lower crossover frequency would be 160-250 Hz and would allow a smaller cabinet.

I developed the amp a few years ago and was surprised how good the transient performance of such a simple design was. I think that performance is partly due to the current drive of the output stage.

The concept makes a virtue of a potential problem. Baxandall pointed out that Transistor Cbc would slow the response. In this case it acts as a free Cdom stabilising the Vas, which is the output stage.

I needed 800 ohm base stopper resistors to make the simulated design work, but they were not needed for the real world (except for the anomalous ST TIP142). I suspect that this is why the real world high frequency distortion was better than 0.1%, whereas the simulated distortion was 0.5%. More work needed to match the simulated to the real results but I leave that to the experts.

It was revealing to look at the op-amp output when the amplifier was giving a full output 20kHz triangle wave. There is a dead band which transitions in 1 to 2uS so you will be blissfully unaware of any problem. The ramps show that the darlingtons have good linearity.

However I was not 100% happy with the voltage regulators as a band-aid fix for the quiescent current with supply voltage variation problem. Hence the design never made it to a dedicated PCB layout from the Veroboard prototype. Nor did I formally post it to Diyaudio. I developed it until it was good enough for my own domestic use, but would not regard it as a “production” design. However the prototype has been happily working for several years so I offer the following ideas which I have not tried for you to experiment with.

The main issue was the quiescent current variation with supply volts. A way around this is to have 2 current setting pots, one for each of the upper and lower halves of the output stage. The current defining resistor is eliminated. Also the voltage regulators are removed. When setting the currents a resistive load is required. R13,14,30 and 31 to be 250 ohm preset pots. R10 and R28 are removed as well as the regulator components.

The current stability would also be improved by defining the op amp voltages with zeners. To lower the self heating effects of the NE5534, the voltage of these would be 12 rather than 15V. R2,3,21 and 22 are now 12V zeners. Also R4,9 ,23,and 27 are 330 ohm.

The thermal feedback would be more consistent if the thermistors were bonded to solder tags and the tags used as the power transistor mounting washers. Nelson Pass uses tagged thermistors in his designs which gave me the idea. Unfortunately Vishay who make tagged or lugged thermistors do not make the value needed here so you have to make your own.

Lastly a R-C filter at the input to limit the bandwidth both for TIM and radio interference reasons would be worth fitting. Put 470pF caps across R1 and R20

I just discovered the reason for the anomalous ST TIP142. The zeptobars website has photos of the silicon dies used for various devices. One of these for the 2STD1665 gave a clue that the device would be fast (too fast for owner!) If you look up the spec for the device it is fast. Curiously ST do not make speed claims for the similar planar base island TIP142

I had to make it a quintet of people beginning with B. Thomas Bayes came up with Bayes’ Theorem, a basic law of probability governing how to modify one’s beliefs when new evidence arrives. Are you Bayesian or Boolean?

In the Boolean worldview, the world is organised into basic situations such as Sydney being north of Melbourne. Such situations are facts. Truth is correspondence to facts. That is, if a belief matches a fact, it is objectively true; if not, it is objectively false. If you and I disagree, one of us must be right, the other wrong; and if I know I’m right, then I know you’re wrong. Totally wrong.

In the Bayesian worldview, beliefs are not simply true or false, but more or less probable. That is, we can be more or less confident that they are true, given how they relate to our other beliefs and how confident we are in them. If you and I disagree about the cause of climate change, it is not a matter of me being wholly right and you being wholly wrong, but about the differing levels of confidence we have in a range of hypotheses. Dare I say it, shades of grey!

Another question, are you Babylonian or Balkan in your Philosophy? Feynman used to say that there were two kinds of Physicists, the Babylonians and the Greeks. He was referring to the opposing philosophies of those ancient civilizations. The Babylonians made western civilization’s first great strides in understanding numbers and equations, and in geometry.
Yet it was the later Greeks – in particular Thales, Pythagoras, and Euclid – whom we credit with inventing Mathematics. This is because the Babylonians cared only whether or not a method of calculation worked – that is, adequately described a real physical situation – and not whether it was exact, or fitted into any greater logical system. Thales and his Greek followers, on the other hand, invented the idea of theorem and proof – and required that for a statement to be considered thorough, it had to be an exact logical consequence of a system of explicitly stated axioms or assumptions. To put it simply, the Babylonians focused on phenomena, the Greeks on the underlying order.”
Nevertheless, the existence of Babylonian method has actually a deep sense: axiomatic approach can be formulated only if satisfactory number of facts, needed for the generalization, is accumulated.

The silicon revolution started at Shockley Semiconductor in April 1956 at Santa Clara which was the year Shockley got the Nobel prize for Physics for inventing the transistor. However by 1957 a number of staff he had recruited left to join Fairchild. More here: